arXiv research

New method learns high-quality Laplacian representations for reinforcement learning.

Paper proves MDS NP-hard and provides a PTAS.

Criteria found for graph drawings on surfaces.

Drawing on some recent results that provide the formalism necessary to definite stationarity for infinite random graphs, this paper initiates the study of statistical and learning questions pertaining to these objects. Specifically, a criterion for the existence of a consistent test for complex hypotheses is presented,…

Rotation systems can't always be drawn in surfaces.

Stress, edge crossings, and crossing angles play an important role in the quality and readability of graph drawings. Most standard graph drawing algorithms optimize one of these criteria which may lead to layouts that are deficient in other criteria. We introduce an optimization framework, Stress-Plus-X (SPX), that sim…

A graph-based sampling and consensus (GraphSAC) approach is introduced to effectively detect anomalous nodes in large-scale graphs. Existing approaches rely on connectivity and attributes of all nodes to assign an anomaly score per node. However, nodal attributes and network links might be compromised by adversaries, r…

Graph convolutional networks (GCNs) suffer from the irregularity of graphs, while more widely-used convolutional neural networks (CNNs) benefit from regular grids. To bridge the gap between GCN and CNN, in contrast to previous works on generalizing the basic operations in CNNs to graph data, in this paper we address th…

New concept of k-holes in simple drawings and convex drawings.

We present sketch-rnn, a recurrent neural network (RNN) able to construct stroke-based drawings of common objects. The model is trained on thousands of crude human-drawn images representing hundreds of classes. We outline a framework for conditional and unconditional sketch generation, and describe new robust training …

SCE improves network embedding using sparsest cut for negative samples only.

There are three main thrusts to this article: a new proof of Levi's Enlargement Lemma for pseudoline arrangements in the real projective plane; a new characterization of pseudolinear drawings of the complete graph; and proofs that pseudolinear and convex drawings of $K_n$ have $n^2+{}$O$(n\log n)$ and O$(n^2)$, respect…

The paper explores invariants of graph drawings in the plane.

A {\em good drawing\/} of $K_n$ is a drawing of the complete graph with $n$ vertices in the sphere such that: no two edges with a common end cross; no two edges cross more than once; and no three edges all cross at the same point. Gioan's Theorem asserts that any two good drawings of $K_n$ that have the same rotations …

We present a simplified exposition of some classical and modern results on graph drawings in the plane. These results are chosen so that they illustrate some spectacular recent higher-dimensional results on the border of topology and combinatorics. We define a mod2-valued self-intersection invariant (i.e. the van Kampe…

New results on splitting tangles and spatial graphs.

CoSE models complex drawings by treating strokes as a collection that can be composed.

In this text I present some problems which led to the introduction of special kinds of graphs as tools for studying singular points of algebraic surfaces. I explain how such graphs were first described using words, and how several classification problems made it necessary to draw them, leading to the elaboration of a s…

Paper analyzes neural network complexity for planning problems.

A novel approach to federated learning with strong privacy guarantees.

Sheaf Neural Networks improve graph learning with geometric insights.

New architectures improve topological deep learning's ability to capture complex data features.

New method synchronizes graphs with probability measures on rotations.

This work generalizes graph neural networks (GNNs) beyond those based on the Weisfeiler-Lehman (WL) algorithm, graph Laplacians, and diffusions. Our approach, denoted Relational Pooling (RP), draws from the theory of finite partial exchangeability to provide a framework with maximal representation power for graphs. RP …

A family of Markov blankets in a faithful Bayesian network satisfies the symmetry and consistency properties. In this paper, we draw a bijection between families of consistent Markov blankets and moral graphs. We define the new concepts of weak recursive simpliciality and perfect elimination kits. We prove that they ar…

Simpler algorithms for morphing planar and toroidal graphs.

Drawing together techniques from combinatorics and computer science, we improve the census algorithm for enumerating closed minimal P^2-irreducible 3-manifold triangulations. In particular, new constraints are proven for face pairing graphs, and pruning techniques are improved using a modification of the union-find alg…

Visual rendering of graphs is a key task in the mapping of complex network data. Although most graph drawing algorithms emphasize aesthetic appeal, certain applications such as travel-time maps place more importance on visualization of structural network properties. The present paper advocates a graph embedding approac…

Recent advances in Quantum Topology assign $q$-series to knots in at least three different ways. The $q$-series are given by generalized Nahm sums (i.e., special $q$-hypergeometric sums) and have unknown modular and asymptotic properties. We give an efficient method to compute those $q$-series that come from planar gra…

We propose a novel model for generating graphs similar to a given example graph. Unlike standard approaches that compute features of graphs in Euclidean space, our approach obtains features on a surface of a hypersphere. We then utilize a von Mises-Fisher distribution, an exponential family distribution on the surface …

Hypothesis testing for graphs has been an important tool in applied research fields for more than two decades, and still remains a challenging problem as one often needs to draw inference from few replicates of large graphs. Recent studies in statistics and learning theory have provided some theoretical insights about …

Topology helps estimate chromatic numbers of random graphs on spheres.

SketchEmbedNet learns image representations from sketches, useful for few-shot learning.

Graph neural networks have become increasingly popular in recent years due to their ability to naturally encode relational input data and their ability to scale to large graphs by operating on a sparse representation of graph adjacency matrices. As we look to scale up these models using custom hardware, a natural assum…

Novel graphical models for time series with latent confounders improve causal inference.

This paper studies semi-supervised object classification in relational data, which is a fundamental problem in relational data modeling. The problem has been extensively studied in the literature of both statistical relational learning (e.g. relational Markov networks) and graph neural networks (e.g. graph convolutiona…

Recent deep learning approaches for representation learning on graphs follow a neighborhood aggregation procedure. We analyze some important properties of these models, and propose a strategy to overcome those. In particular, the range of "neighboring" nodes that a node's representation draws from strongly depends on t…

The aim of this short note is to draw attention to a method by which the partition function and marginal probabilities for a certain class of random fields on complete graphs can be computed in polynomial time. This class includes Ising models with homogeneous pairwise potentials but arbitrary (inhomogeneous) unary pot…

The paper introduces a new loss function to prevent overfitting in semi-supervised graph networks.

A framework for hypothesis testing on attributed graphs using sampling.

We investigate the problem of sequentially predicting the binary labels on the nodes of an arbitrary weighted graph. We show that, under a suitable parametrization of the problem, the optimal number of prediction mistakes can be characterized (up to logarithmic factors) by the cutsize of a random spanning tree of the g…

This paper tackles exact recovery of clusters in a stochastic Ising model on a SBM graph.

YOASOVI improves stochastic VI for large models with fast, self-correcting sampling.

The paper defines invariants for almost graph embeddings and explores their properties.

Graph representations offer powerful and intuitive ways to describe data in a multitude of application domains. Here, we consider stochastic processes generating graphs and propose a methodology for detecting changes in stationarity of such processes. The methodology is general and considers a process generating attrib…

Graph neural networks detect anomalies in object-centric business processes.

This paper optimizes object tracking on edge devices with small matrices.

Polynomial bound on tightening curves on surfaces without increasing crossings.